Related papers: Evolutionary Algorithm for Graph Coloring Problem
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
Coloring is one of the most famous problems in graph theory. The coloring problem on undirected graphs has been well studied, whereas there are very few results for coloring problems on directed graphs. An oriented k-coloring of an oriented…
This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…
Many complex systems and datasets are characterized by multiway interactions of different categories, and can be modeled as edge-colored hypergraphs. We focus on clustering such datasets using the NP-hard edge-colored clustering problem,…
The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…
In this paper, we consider the maximum $k$-edge-colorable subgraph problem. In this problem we are given a graph $G$ and a positive integer $k$, the goal is to take $k$ matchings of $G$ such that their union contains maximum number of…
A star edge coloring of a graph $G$ is a proper edge coloring with no 2-colored path or cycle of length four. The star edge coloring problem is to find an edge coloring of a given graph $G$ with minimum number $k$ of colors such that $G$…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
For a positive integer $k$, a $k$-colouring of a graph $G=(V,E)$ is a mapping $c: V\rightarrow\{1,2,...,k\}$ such that $c(u)\neq c(v)$ whenever $uv\in E$. The Colouring problem is to decide, for a given $G$ and $k$, whether a $k$-colouring…
This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e.\ with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so…
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…
This paper explores the application of a new algebraic method of color exchanges to the edge coloring of simple graphs. Vizing's theorem states that the edge coloring of a simple graph $G$ requires either $\Delta$ or $\Delta+1$ colors,…
Given a graph $G=(V,E)$, the $b$-coloring problem consists in attributing a color to every vertex in $V$ such that adjacent vertices receive different colors, every color has a $b$-vertex, and the number of colors is maximized. A $b$-vertex…
The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
A well-studied coloring problem is to assign colors to the edges of a graph $G$ so that, for every pair of vertices, all edges of at least one shortest path between them receive different colors. The minimum number of colors necessary in…
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve…
The problem of finding the minimum number of colors to color a graph properly without containing any bicolored copy of a fixed family of subgraphs has been widely studied. Most well-known examples are star coloring and acyclic coloring of…
List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded…